I have a T3 CTR in .223 (1-8 twist rate, which most newer Tikka's in .223 have) and have had success with 60gr Hornady VMAX and Berger 60gr Flat Base Varmint (handloads), which shoot tighter groups and produce lower standard deviation numbers than the 70+ grain bullets (with my particular Tikka CTR).
For factory ammunition I would suggest Hornady Black 62gr FMJ or Hornday 68gr BTHP Match. Berger does produce 73gr BT Target ammunition, but it is about $50 a box versus the $25. for the Hornady Black.
If you have a 1-10 or 1-12 twist rate, then lighter (55gr and under) ammunition should shoot well, like Hornady 53gr Superformance Varmint, or Sierra Prairie Enemy 55gr.